As noted in the previous post, having someone else pick up the car will probably be difficult to impossible.
I have a PDF of the Amex standard policy ( the one that is free when you use your Amex to rent the car), there is also a premium additional cost coverage that might have different provisions. PM me if you want me to email it to you.
I don't see anything in the policy that would exclude any authorized driver, whether identified by name on the rental agreement or not. This seems to be the most relevant clause:
Losses Not Covered
...
operation of the Rental Auto in violation of the terms and conditions of the Rental Company agreement (including but not limited to losses occurring when: a person not permitted to operate the vehicle pursuant to terms of the rental agreement was in possession or control of the vehicle; or, driving the vehicle outside of the authorized rental territory);
This clause might be limiting, however:
Coverage continues in effect while the Cardmember remains in control and possession of the Rental Auto. A Cardmember, who is physically challenged and unable to operate the Rental Auto, may be the Primary Renter if he/she is the Cardmember entering into the rental transaction.